Bus architecture for quantum processing

ABSTRACT

A quantum processing apparatus includes a qubit, a superconducting bus, and a controllable coupling mechanism that controllably couples the superconducting bus to the qubit. The controllable coupling mechanism is characterized by a first state in which the superconducting bus and the qubit are capacitively coupled, thereby permitting a coupling operation to be performed between a quantum device, coupled to the superconducting bus, and the qubit. The controllable coupling mechanism is also characterized by a second state in which the superconducting bus and the qubit are capacitively uncoupled such that the qubit and the quantum device are not coupled to each other.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit, under 35 U.S.C. § 119(e), of U.S.Provisional Patent Application No. 60/556,778, filed on Mar. 26, 2004,which is hereby incorporated by reference in its entirety. Thisapplication is further related to concurrently filed application Ser.No. 11/089,650, entitled “Methods for Quantum Processing,” which ishereby incorporated in its entirety.

1. FIELD OF THE INVENTION

The present invention relates to quantum computing and superconductingdevices. More specifically, the present invention relates to performingoperations on superconducting qubits.

2. BACKGROUND OF THE INVENTION

Several quantum computing hardware proposals have been made. Of thesehardware proposals, the most scalable physical systems appear to bethose that are superconducting structures. Superconducting material ismaterial that has no electrical resistance below critical levels ofcurrent, magnetic field and temperature. Josephson junctions areexamples of such structures.

2.1 Superconducting Qubits

One physical realization of a quantum computer is based on quantum bits,known as “qubits.” Generally speaking, a qubit is a well-definedphysical structure that (i) has a plurality of quantum states, (ii) canbe coherently isolated from its environment, and (iii) permits quantumtunneling between two or more quantum states associated with the qubit.See for example, Mooij et al., 1999, Science 285, p. 1036, which ishereby incorporated by reference. Representative but nonlimitingphysical implementations of qubits include ion traps, cavity quantumelectrodynamics (QED), nuclear magnetic resonance (NMR) based qubits,neutral atoms in an optical lattice, quantum dots, silicon based qubits,nuclear spin of single donor atoms in silicon (Kane computer), electronson liquid helium, optical photons, and superconducting Josephsonjunction devices. A survey of the current physical systems from whichqubits can be formed is found in Braunstein and Lo (eds.), 2001,Scalable Quantum Computers, Wiley-VCH Verlag GmbH, Berlin, which ishereby incorporated by reference in its entirety. In order for aphysical system to support quantum computation, specific requirementsmust be satisfied:

-   -   the physical system must be scalable and composed of well        characterized qubits (scalability requirement);    -   an ability to initialize the state of such qubits to a simple        fiducial state, such as |000 . . .        ;    -   long relevant decoherence times for such qubits, much longer        than the gate operation time used to manipulate the quantum        states of the qubits in order to perform quantum computations;    -   a “universal” set of such quantum gates; and

a qubit-specific measurement capability in order to measure the statesof the qubits.

See DiVincenzo in Scalable Quantum Computers, chapter 1, Wiley-VCHVerlag GmbH, Berlin, which is hereby incorporated by reference in itsentirety. The scalability requirement means that it must be possible tocouple a reasonable number of the qubits in a way that prevents thequbits from decohering and thereby losing their quantum nature. Suchcoupling is referred to in the art as coherent coupling. Associated withscalability is the need to eliminate qubit decoherence.

Also required for a qubit to be useful in quantum computing is theability to perform operations that initialize, control, and couple thequbit. Control of a qubit includes performing single qubit operations ona single qubit (single qubit gates). Such control further includesperforming multi-qubit operations on two or more qubits (multi-qubitgates). This set of operations is typically a universal set. A universalset of quantum operations is any set of quantum operations that permitsall possible quantum computations. Many sets of gates (operations) areuniversal. For example, single qubit and CNOT gates can be used toimplement an arbitrary unitary operation on n qubits, and therefore areuniversal for quantum computation. See Barenco et al., 1995, Phys. Rev.A 52, p. 3457 and Nielsen and Chuang, 2000, Quantum Computation andQuantum Information, Cambridge University Press, Cambridge, pp. 188-202,each of which is hereby incorporated by reference in its entirety.

Many qubits include Josephson junctions. There are two principal meansto realize superconducting qubits using such Josephson junctions. Onemeans corresponds to the limits of well-defined charge (charge qubit).The other means corresponds to the limits of well-defined phase (phasequbit). Phase and charge are related variables that, according tocentral quantum principles, are canonical conjugates of one another. Incharge qubits, the charging energy of a superconducting island dominatesover the Josephson energy (E_(C)>>E_(J)) and the relevant quantum degreeof freedom is the charge on superconducting islands. As used herein, thesymbol >> means that the physical variable that precedes the >> symbol,the first physical variable, is so much larger than the physicalvariable that comes after the >> symbol, the second physical variable,that the observable range in magnitudes of the second physical variableis negligible relative to the magnitude of the first variable. In fluxqubits, the Josephson energy dominates over the charging energy(E_(J)>>E_(C)) and the relevant quantum degree of freedom is magneticflux. The division of the two classes of devices is outlined in Makhlinet al., 2001, Rev. Mod. Phys. 73, pp. 357-491, which is herebyincorporated by reference in its entirety. Superconducting qubitsinclude devices that are well known in the art, such as Josephsonjunctions. See, for example, Barone and Paternò, 1982, Physics andApplications of the Josephson Effect, John Wiley and Sons, New York;Martinis et al., “Rabi oscillations in a large Josephson junctionqubit,” preprint presented at the American Physical Society (APS) 2002Annual Meeting, held Jul. 27-31, 2002; and Han et al., 2001, Science,293, 1457, each of which is hereby incorporated by reference in itsentirety.

Materials that exhibit superconducting properties are candidates forquantum computing applications, since the quantum behavior of the Bosecondensates (Cooper pairs) at Josephson junctions has macroscopicallyobservable variables. Indeed, several designs of a superconducting qubithave been proposed and tested, such as charge qubits, rf-SQUID, andthree-junction flux qubits. See, for example, Nakamura et al., 1999,Nature 398, pp. 786-788; Friedman et al., 2000, Nature 406, pp. 43-46;and van der Wal et al., 2000, Science 290, pp. 773-777, each of which ishereby incorporated by reference in its entirety. The qubits describedin these references are not coupled to each other and are not controlledin a scalable manner. Therefore, the qubits described in thesereferences do not satisfy all the requirements for universal quantumcomputing put forth by DiVincenzo.

2.2 Coherence Requirement

The quantum mechanical properties of a qubit are affected byinteractions between the qubit and the environment (e.g., othersystems). Yet quantum computation requires that the qubits that make upthe physical quantum computation system be isolated from suchinteractions so that the state of the qubits can coherently evolve inaccordance with quantum gates that are applied to the qubits. Despitethe requirement for isolation so that qubits can evolve, universalquantum computing still requires some control over (interaction with)the qubits so that fundamental operations such as qubit initialization,gate application, and qubit state measurement can be effected. Thisapparent contradiction between the need for isolation and the need forcontrol over the qubits is a direct result of the quantum behavior ofqubits.

The need for isolated qubits that nevertheless can be controlled haspresented fabrication and design challenges including identification ofmethods for initialization, control, coupling and measurement of qubits.Systems and methods for addressing these challenges are beinginvestigated. For instance, systems in which qubits can be controlledand measured in ways that do not perturb their internal quantum statesare being sought. Devices that include multiple controllable qubits thatpermit classical logic operations to be performed are central to thegoal of building a quantum computer. To date, many known systems andmethods for coupling model qubits in simulated quantum computing deviceshave been unwieldy and generally unsatisfactory. Such systems andmethods are based on optics (entanglement of photons) or nuclearmagnetic resonance (utilizing spin states of atoms and molecules).

Recently, however, inductive coupling between phase qubits has beendescribed in, for example, Orlando et al., 1999, “SuperconductingPersistent Current Qubit,” Phys. Rev. B 60, p. 15398; and Makhlin etal., 2001, “Quantum-State Engineering with Josephson-Junction Devices,”Rev. Mod. Phys. 73, pp. 357400, in particular, page 369, each of whichis hereby incorporated by reference in its entirety. However, the qubitsdescribed in Orlando et al. and Makhlin et al. have the drawback thatthey have not been coupled and controlled in a scalable manner.

2.3 Gate Operations

As discussed above, in order to effect quantum computing, a physicalsystem containing a collection of qubits is needed. A qubit, as definedherein, is a quantum two-level system analogous to the ground and firstexcited state of an atom. The first state of a qubit is denoted as |0

and the second state is denoted as |1

. A feature that distinguishes a qubit from a bit is that, according tothe laws of quantum mechanics, the permitted states of a single qubitfills up a two-dimensional complex vector space; the general notation iswritten a|0

+b|1

, where a and b are complex numbers. The general state of two qubits,a|00

+b|01

+c|10

+d|11

is a four-dimensional state vector, one dimension for eachdistinguishable state of the two qubit system. When a two-qubit gateoperation has been performed between the two qubits, their states can beentangled during the evolution of that gate. This means that the stateof the two qubits cannot be expressed as a product of the states of twoindividual qubits. The general state of n entangled qubits is thereforespecified by a 2^(n)-dimensional complex state vector. The creation of2^(n)-dimensional complex vectors provides a basis for the computingpotential of quantum computers. For more information on qubits and gateoperations, see Braunstein and Lo (eds.), 2001, Scalable QuantumComputers, Wiley-VCH, New York, which is hereby incorporated byreference in its entirety.

In standard model quantum computation, also known as circuit modelquantum computation, quantum gate operations are performed on the qubitsin the time domain. Gates are represented by matrices that are matrixmultiplied with the qubit's state vector. The elementary single-qubitgates are:

${X = \begin{bmatrix}0 & 1 \\1 & 0\end{bmatrix}},\mspace{14mu}{Y = \begin{bmatrix}0 & {- i} \\i & 0\end{bmatrix}},\mspace{14mu}{{\text{and}\mspace{14mu} Z} = {\begin{bmatrix}1 & 0 \\0 & {- 1}\end{bmatrix}.}}$Other single-qubit gates include, but are not limited to:

${H = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}},\mspace{14mu}{S = \begin{bmatrix}1 & 0 \\0 & i\end{bmatrix}},\mspace{14mu}{{\text{and}\mspace{14mu} T} = {\begin{bmatrix}1 & 0 \\0 & {\mathbb{e}}^{{\mathbb{i}}\;\pi\text{/}8}\end{bmatrix}.}}$There are also two-qubit quantum gate operations, which are performedbetween two qubits. These two-qubit gates are represented by 4×4matrices. Examples of two-qubit gates are CNOT, SWAP, and √{square rootover (SWAP)} Certain combinations of one- and two-qubit gates are allthat are necessary to construct a universal set of gates for quantumcomputing. An example of such a universal set is X, Z, and CNOT. Anotherexample of a universal set is X, Y, and √{square root over (SWAP)}.These gates alone are said to be universal for quantum computation, andcan thus implement any unitary operation on n qubits. These groupings ofgates are said to be universal because the single qubit gates cangenerate the SU(2) group, while the two-qubit gate can generate theSU(2^(N)) group. SU(2) describes the states of a single qubit. See, forexample, U.S. Patent Application Publication No. 2004/238813 A1,entitled, “Dressed Qubits,” which is hereby incorporated by reference inits entirety.

To make a practical design for a quantum computer, one decomposes anyvalid quantum computation into a sequence of elementary one- andtwo-qubit quantum gates that can be realized in physical hardware thatis feasible to fabricate. The set of these one- and two-qubit gates isarbitrary provided it is universal, e.g., capable of achieving any validquantum computation from a quantum circuit comprising only gates fromthis set. A widely accepted method of operating quantum computers is the“standard paradigm” of universal quantum computation. According to thestandard paradigm, all operations necessary for a quantum computer canbe performed by appropriate application of a set of single qubit gatesand one two-qubit gate because these operations generate the fullspecial unitary 2 group, denoted SU(2^(N)), and span the space necessaryfor quantum computation.

A group G, such as the SU(2^(N)) group, is a finite or infinite set ofelements together with a binary operation that together satisfy the fourfundamental properties of closure, associativity, the identity property,and the inverse property. The operation with respect to which a group isdefined is often called the “group operation,” and a set is said to be agroup “under” this operation. In other words, elements A, B, C, . . . ofset S, with binary operation between A and B, denoted AB, form a group Gwhen they have the following properties:

(i) closure: if A and B are two elements in S, then the product AB isalso in S;

(ii) associatively: the defined multiplication is associative, e.g., forall A, B, CεS, (AB)C=A(BC);

(iii) identity: there is an identity element I (a.k.a., 1, E, or e) suchthat IA=AI=A for every element AεS; and

(iv) inverse: there is an inverse or reciprocal of each element.Therefore, the set S contains an element B=A⁻¹ such that AA⁻¹=A⁻¹A=I foreach element of S.

The SU(2^(N)) group satisfies these conditions. The SU(2^(N)) group is asubset of unitary 2. Unitary 2 is a group where the objects are 2 by 2matrices that are unitary, e.g., UU†=1, and the operation is matrixmultiplication. SU(2^(N)) has the general group element

$U = \begin{pmatrix}a & b \\{- b^{*}} & a^{*}\end{pmatrix}$with a×a*+b×b*=1 and where a and b are complex. For more information onspecial unitary groups, see Arfken, 1985, Mathematical Methods forPhysicists, Third Edition, Academic Press, Inc., San Francisco, which ishereby incorporated by reference in its entirety.

Quantum computers that generate the full SU(2^(N)) group space for Nqubits are sometimes referred to as universal quantum computers. Inparticular, two single qubit gates that are based on two non-commutatingHermitian operators can generate all one-qubit quantum gates. Two qubitgates can entangle the states of two qubit quantum systems.

A common example of a two-qubit gate is the controlled NOT (CNOT) gate.The CNOT gate has two input qubits, known as the control qubit and thetarget qubit, respectively. In a CNOT gate, if the control qubit is setto 0, then the target qubit is left alone. If the control qubit is setto 1, then the target qubit is flipped. However, any classical (e.g.AND) or quantum (e.g. σ_(z)

σ_(z)) two qubit logic gate classical (e.g. AND) or quantum (e.g. σ_(z)

σ_(z)) can be used. Alternatively, one can use a discrete set of singlequbit operations that can approximate, to arbitrary accuracy, anyquantum gate. An example of a discrete set of logic gates is, HADAMARD,PHASE (or S), π/8 (or T), and an entangling gate such as CNOT. SeeNielsen and Chuang, 2000, Quantum Computation and InformationProcessing, Cambridge University Press, which is hereby incorporated byreference in its entirety.

A CNOT gate is composed of an elementary two-qubit gate operation suchas σ_(z)

σ_(z) and some other single qubit operations. Operators X, Z, and σ_(z)

σ_(z), correspond to the elementary set of gates of many solid-statedesigns and can be implemented in NMR-based quantum computers. SeeGershenfeld and Chuang, 1997, Science 275, p. 351, which is herebyincorporated by reference in its entirety. Implementation of OperatorsX, Z, and σ_(z)

σ_(z) in a quantum register is described in Zagoskin and Blais, 2000,Phys. Rev. A 61, 042308, which is hereby incorporated by reference inits entirety.

Another elementary two-qubit operation is σ_(x)

σ_(x). Normally a system has only one natural interaction, σ_(z)

σ_(z) or σ_(x)

σ_(x), which is the elementary quantum gate that acts on two qubitswhenever two qubits are coupled, in a given system. This elementary gateoperation is then used, in combination with elementary single-qubit gateoperations, to form two-qubit gates such as CNOT, SWAP, etc. Asindicated above, two elementary two-qubit gate operations are:

${{\sigma_{z} \otimes \sigma_{z}} = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & {- 1} & 0 & 0 \\0 & 0 & {- 1} & 0 \\0 & 0 & 0 & 1\end{bmatrix}},\mspace{14mu}{{\sigma_{x} \otimes \sigma_{x}} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0\end{bmatrix}}$Performing a coupling operation between qubits comprises performing anelementary two-qubit gate operation, such as σ_(z)

σ_(z) or σ_(x)

σ_(x), on two qubits.

In some instances, elementary gate operations acting on one or morequbits will leave the qubits entangled, or unentangled following theoperation. In some instances, an elementary gate operation causes thequbits on which the gate was applied to become unentangled.

Current methods for performing two qubit gate operations on qubits inorder to perform quantum computing are susceptible to loss of coherence.Loss of coherence can be viewed as the loss of the phases of quantumsuperpositions in a qubit as a result of interactions with theenvironment. Loss of coherence results in the loss of the superpositionof states in a qubit. See, for example, Zurek, 1991, Phys. Today 44, pp.36-44; Leggett et al., 1987, Rev. Mod. Phys. 59, pp. 1-85; Weiss, 1999,Quantitative Dissipative Systems, 2^(nd) ed., World Scientific,Singapore; and Hu et al.; arXiv.org: cond-mat/0108339v2, each of whichis hereby incorporated by reference in its entirety.

2.4 Use of a Resonant Controlled Qubit System (RCQS) to Enable Two-QubitCoupling Operations

It has been proposed in the art that a superconducting resonator can becoupled with a qubit when the resonant frequency of the superconductingresonator is correlated with the energy difference between the basisstates of the qubit. Once coupled, coupling operations can be performed.See, for example, Buisson and Hekking, Aug. 18, 2000, “Entangled statesin a Josephson charge qubit coupled to a superconducting resonator,”arXiv.org: cond-mat/0008275v1; and Al-Saidi and Stroud, Dec. 4, 2001,“Eigenstates of a small Josephson junction coupled to a resonantcavity,” Phys. Rev. B 65, 014512, which are hereby incorporated byreference in their entireties. The entanglement proposed in thesereferences causes the state of the charge qubit to be entangled with thestate of the superconducting resonator, thus illustrating the potentialfor achieving entangled quantum states in a solid state design. However,the references do not provide methods for coherently performing couplingoperations on qubits in a solid-state design, nor do they demonstratehow such coupling can be used to facilitate quantum computing.

The quantum computing systems and methods described in U.S. patentapplication Ser. No. 10/419,024, filed May 17, 2003, entitled “ResonantControlled Qubit System,” as well as in U.S. patent application Ser.Nos. 10/798,737, 10/801,335, and 10/801,340, which are herebyincorporated by reference in their entireties, overcome some of thelimitations of Buisson and Hekking as well as Al-Saidi and Stroud. Thesepatent applications describe systems and methods for coupling qubitstogether in a manner that overcomes the requirements of direct couplingand furthermore realize a bus system for coupling non-adjacent qubitstogether. FIG. 1 illustrates such a system 700. In system 700, bus 990is capacitively coupled to respective qubits 610 by respectivecapacitors 611-E. Each qubit 610 is a superconducting quantronium qubithaving a mesoscopic island region 670 separated from leads by Josephsonjunctions 615 and capacitors 611. Charge devices 662 are used tomaintain the potential energy profile of a corresponding quantroniumqubit 610 in a regime that can be used for quantum computation. Thequantum energy state of each quantronium qubit 610 is determined (readout) by a corresponding readout device 650.

A microwave signal with the appropriate frequency can cause transitionsbetween the basis states of qubits 610, hence providing manipulation ofthe qubit state. See Vion et al., 2002, Science 296, pp. 886-889,hereinafter referred to as Vion et al., which is hereby incorporated byreference in its entirety. In FIG. 1, the microwave signal is applied bycorresponding A/C voltage sources 661, which emit one or morefrequencies in the microwave range. Qubits 610-1 through 610-N areelectrically coupled to bus 990 in such a manner that resonant controlsystem 920, which is coupled to (in electrical communication with) thequbits through bus 990, can be used to mediate coupling operationsbetween qubits 610. As illustrated in FIG. 1, resonant control system920 includes current source 921-1, Josephson junction 921-2, shuntcapacitance 921-3, and ground 930 _(q),

There is a limit to how many qubits 610 can be capacitively orinductively connected to bus 990 in the configuration illustrated inFIG. 1. To address this limitation, U.S. patent application Ser. No.10/419,024, filed May 17, 2003, entitled “Resonant Controlled QubitSystem,” referred to hereinafter as Blais et al and which is herebyincorporated by reference in its entirety, proposed dividing bus 990into sections using switches and, optionally, pivot qubits asillustrated in quantum register 800 (FIG. 2A). Quantum register 800includes a plurality of qubits 610 and a plurality of resonant controlsystems 920. Qubits 610 in quantum register 800 are separated intogroups 802. Each group 802 of qubits is associated with a respectiveresonant control system 920. Each group 802 of qubits is connected to aswitch 991 that typically is in an open state, thereby isolating thequbits of one group 802 from other groups 802 linked to bus 990. In someinstances, switches 991 are superconducting single electron transistors(SSETs). The characteristics of SSETs are known and are described, forexample, in Joyez et al., 1994, Phys. Rev. Lett. 72, pp. 2458-2461,which is hereby incorporated by reference in its entirety. Fabricationof SSETs is known in the art. For example, see Born et al., 2001, IEEETrans. Appl. Superconductivity 11, pp. 373-376, which is herebyincorporated by reference in its entirety. As illustrated in FIG. 2A, apivot qubit 610-P is placed in regions 990-P that interface respectivequbit groups 802. Pivot qubits 610-P facilitate interaction betweenqubits in different qubit groups 802. In FIG. 2A, each qubit 610 isrespectively associated with a device 660. Each respective device 660 isa mechanism for controlling the quantum state of the corresponding qubit610.

Blais et al. provides methods for performing a coupling operationbetween a first qubit 610 in a first qubit group 802 and a second qubit610 in a second qubit group 802. In step 1000 of a method disclosed inBlais et al., a first qubit 610 in a first group 802 is coupled to afirst resonant control system 920 by biasing system 920 to a frequencyω₁₂ that represents the energy differential between a first quantumenergy level and a second quantum energy level (e.g., the lowest twoquantum energy levels) of the first qubit 610. During step 1000, thefirst qubit group 802 is isolated from other qubit groups 802 by openingall switches 991 that connect the first qubit group 802 to other qubitgroups 802. In step 1000, the first resonant control system 920 is tunedto a frequency ω₁₂ for a time that is sufficiently long enough toperform a coupling operation between the first resonant control system920 and the first qubit 610.

In step 1002 of the method, a first switch 991 between the first qubitgroup 802 and a region 990-P that adjoins the second qubit group 802 isclosed so that first resonant control system 920 will couple to a firstpivot qubit 610-P. To achieve this coupling, the first resonant controlsystem 920 is biased to a frequency ω_(P) that represents the energydifferential between a first quantum energy level and a second quantumenergy level (e.g., the lowest two quantum energy levels) of first pivotqubit 610-P so that the quantum state of first resonant control system920 couples with the quantum state of first pivot qubit 610-P. Duringstep 1002, a second switch 991 that electrically connects first pivotqubit 610-P to a second qubit group 802 is in an open state, therebyisolating the first pivot qubit 610-p from a second resonant controlsystem 920. Next, first switch 991 is opened, thereby isolating thefirst pivot qubit 610-P from the first qubit group 802.

In step 1004, second switch 991 (e.g., 991-2) is closed. This allowspivot qubit 610-P to couple with the second resonant control system 920(e.g., 920-2). To achieve this coupling, second resonant control system920 is biased to a frequency ω_(P) that represents the energydifferential between a first quantum energy level and a second quantumenergy level (e.g., the lowest two quantum energy levels) of pivot qubit610-P (e.g., 610-P-i), thereby coupling pivot qubit 610-P and secondresonant control system 920. In step 1006, the second switch 991 isopened, thereby isolating the second qubit group 802 from the firstpivot qubit 610-P.

In step 1008, the second resonant control system 920 (e.g., 920-2) iscoupled to a desired second qubit 610 (e.g., 610-3). This isaccomplished by tuning the second resonant control system 920 to afrequency ω₃₄ for some time period t₁₀₀₈. The frequency ω₃₄ representsthe energy differential between a first quantum energy level and asecond quantum energy level of the second qubit (e.g., the lowest twoquantum energy levels) of the desired second qubit 610 so that thequantum state of the second resonant control system 920 is coupled tothe desired second qubit 610. If the desired second qubit 610 is notfound in the second group 802, then steps 1002 through 1006 can berepeated using one or more additional pivot groups 610 until the desiredqubit group 802 is reached. Typically, the respective energydifferentials between the lowest two quantum energy levels of each qubit610 in a given group 802 are unique. Furthermore, the energydifferential between the lowest two quantum energy levels of a pivotqubit should be different than the respective energy differentialbetween the lowest two quantum energy levels of each qubit in each group802 that the pivot qubit 610 is capable of electrically communicatingwith through a switch 991.

2.5 Limits to the Number of Qubits that can be Connected to a Bus

One consideration when designing a quantum computer is the provision ofa circuit architecture that will scale to larger numbers of qubits,beyond the one or two qubit schemes typically found in the known art.Section 2.4 described a promising resonant controlled qubit system(RCQS) for performing coupling operations between qubits connected to abus. However, an important aspect of the RCQS is that, although thequbits are controllably coupled, the number of qubits connected to eachbus segment is limited in part by the effective bus capacitance, whichgrows in proportion with the number of qubits connected to each bussegment. As the capacitance of the bus increases, coupling operationsbecome more difficult to perform in a short enough period of time. Thisgrowth in capacitance is understood when it is appreciated that eachqubit or resonator attached to the bus in the RCQS is attached to groundas illustrated in FIG. 2B, meaning that all the devices are in parallel.Thus, the capacitance C_(bus segment) of a bus segment 990 is determinedby adding up the capacitances of each qubit and resonator attached tothe bus segment:C _(bus segment) =C _(qubit1) +C _(qubit2) + . . . +C _(qubitN) +C_(resonator)  (1)The capacitance of each additional qubit added to a given bus segment inthe RCQS causes that overall capacitance of the bus segment to reach acapacitance threshold that will no longer support quantum computingoperations. For exemplary devices, C_(resonator)=5.8 pF, andC_(qubit)=5.5 fF. Qubits can be added to the bus, so long as the totalsum of the qubit capacitances does not approach C_(resonator). In someembodiments, 10-100 qubits can be added to bus 990 before the sum of thequbit capacitances approaches the capacitance of the resonator andadversely affects the operation of the bus.

As the number of qubits added to the bus increases, another factorbegins to limit the total number of qubits that can be coupled to thebus. This factor is a leakage of the quantum state of the bus to higherbus states as more qubits are added. In other words, as more qubits areadded to the bus, the total Hilbert space becomes proportionally larger,leaving more room for leakage. Thus, operations must be run at a slowerrate to avoid spurious transitions when the number of qubits coupled tothe bus increases in order to avoid such leakage. This isdisadvantageous because all qubits, regardless of design, have a finitecoherence length. Therefore, what is desired in the art are quantumcomputing architectures that can perform quantum computing operationsquickly before the qubits in the architecture decohere.

The RCQS design also has the drawback that it requires that each of thequbits have different energy level spacings (between the informationbasis states). Further still, as discussed in Section 2.4, the method ofcoupling qubits involves a sequence of tuning steps where the energylevel spacing of the respective qubits is tuned to a predetermined valueto match the target qubit and hence realize the desired couplingoperation. To avoid tuning the qubits themselves and hence increasingtheir decoherence, the RCQS introduces a tunable bus to mediate thecoupling operations between qubits. Another limitation of the bus sizein the RCQS arises due to variance in the relative energy level spacingof the qubits. Although each type of qubit can have a different energylevel spacing between a first energy state and a second energy state,from about 800 megahertz (MHz) to about 100 gigahertz (GHz), thepossible values for a given type of qubit fall within a relatively smallrange, for example, a few GHz. If any two or more qubits within a bussegment have similar energy level spacings, then the method will requiretuning one of the qubits away from their operating point, henceincreasing susceptibility to noise for the respective qubits.

Thus, although the segment and pivot architecture illustrated in FIG. 2and as proposed in the RCQS (Blais et al.) represents a significantadvancement over previous multi-qubit coupling proposals, the number ofqubits connected to each segment of the RCQS is potentially limited.Since each pivot operation introduces overhead in the number ofoperations required to couple two qubits together, there is a need toincrease the number of qubits in each segment without compromising thefunctionality of the bus architecture.

3. SUMMARY OF THE INVENTION

The present invention allows a plurality of qubits to be connected to asuperconducting bus in a controllable fashion. Because the connection iscontrollable, each respective qubit in the plurality of qubitscontributes no capacitance or very little capacitance to the bus whenthe quantum state of the qubit is not coupled to the superconductingbus. In this way, more qubits can be attached to the superconducting buswithout increasing the overall capacitance of the bus beyond a thresholdcapacitance that no longer supports coherent quantum computation in areasonable time frame. Also, the qubits are free to have the sameenergy-level spacing, as the coupling is controlled not by tuning theenergy level spacing in the qubits or in a resonator but by tuningcontrollable coupling elements. This provides the additional benefit ofreducing the complexity, and therefore cost, of the inventive quantumarchitectures relative to known quantum systems.

One particular embodiment of the present invention comprises a busarchitecture, capable of interfacing with superconducting qubits andscaling to large numbers of qubits, to create an integrated circuitquantum processor. The superconducting bus is controllably coupled toeach superconducting qubit and is capable of supporting a quantum stateand mediating quantum operations. In some embodiments of the presentinvention, a mechanism for controllable coupling is used to coherentlycouple a qubit to a superconducting bus so that the qubit-buscapacitance is zero or nearly zero when the mechanism for controllablecoupling is uncoupled. This permits a one-dimensional, two-dimensional,or three-dimensional array of qubits to be formed using a single buswithout deterioration of the operation of the bus due to excessive buscapacitance.

In some embodiments of the present invention, a superconducting busarchitecture is grouped into bus segments. Each bus segment is connectedby a pivot segment. Each such pivot segment has a mechanism forcontrollably coupling the pivot segment to one or more bus segments inthe bus architecture. In some embodiments, the mechanism forcontrollable coupling comprises a tunable capacitance, such that thecapacitance is tuned to zero or nearly zero when the pivot segment isdisconnected from the respective bus segment. Thus, in some embodimentswhere the bus is organized into bus segments, each such bus segmentincludes a plurality of qubits and is separated from adjacent bussegments by one or more pivot segments.

In accordance with an embodiment of the present invention, anarchitecture comprising a first qubit and a second qubit, capable ofinteracting with each other in a coupling operation, has a mechanism forcontrollably coupling the first qubit or the second qubit to asuperconducting bus. This mechanism for controllably coupling acorresponding qubit to the superconducting bus has a coupled state inwhich a coupling operation between the corresponding qubit and thesuperconducting bus is possible, and an uncoupled state, in which thecorresponding qubit does not capacitively affect the superconductingbus. In an embodiment of the present invention, a method for performinga coupling operation between a first qubit and a second qubit in aquantum register, in which one or both of the first qubit and the secondqubit is connected to a superconducting bus through a correspondingmechanism for controllable coupling, comprises selecting the first andsecond qubits by tuning the mechanism for controllable coupling to acoupled state. In some embodiments, the first qubit has a mechanism forcontrollable coupling and the second qubit has a direct connection tothe bus.

Some embodiments of the present invention provide a method forperforming a quantum operation comprising (i) coupling a qubit and asuperconducting bus to each other, (ii) tuning a characteristic of thesuperconducting bus for a first period of time, and (iii) uncoupling thequbit and the superconducting bus from each other. In some embodimentsof the present invention, the tuning comprises tuning a quantum devicethat is coupled to the superconducting bus. In some embodiments, thecharacteristic is an energy level spacing in a quantum device. In someembodiments of the present invention, the tuning further comprisessetting either a gate voltage directly applied to a quantum deviceattached to the bus, in the case of a phase-charge qubit for example, ora bias current directly applied to the quantum device attached to thebus, in the case of a current biased Josephson junction for example.

One embodiment of the present invention is a quantum processingapparatus comprising a superconducting qubit, a superconducting bus, aquantum device coupled to the superconducting bus, and a controllablecoupling mechanism that controllably couples the superconducting bus tothe superconducting qubit. The controllable coupling mechanism iscapable of being in any one of a plurality of states at any given time,these plurality of states include a first state in which thesuperconducting bus and the superconducting qubit are capacitivelycoupled and a second state in which the superconducting bus and thesuperconducting qubit are capacitively uncoupled.

Another embodiment of the present invention comprises a bus architecturefor quantum processing, comprising a plurality of bus segments, aplurality of qubit sets, a plurality of pivot segments and a pluralityof controllable coupling mechanisms. Each qubit set in the plurality ofqubit sets comprises a plurality of qubits. Each pivot segment in theplurality of pivot segments controllably couples a different first bussegment and second bus segment in the plurality of bus segments to eachother. Each respective controllable coupling mechanism in the pluralityof controllable coupling mechanisms controllably couples a correspondingqubit in a qubit set to a bus segment in the plurality of bus segmentssuch that each qubit in each qubit set in the plurality of qubit sets iscontrollably coupled to at least one bus segment. Each respectivecontrollable coupling mechanism in the plurality of controllablecoupling mechanisms includes a coupled state, wherein a controllablecoupling operation between a bus segment in the plurality of bussegments and a qubit corresponding to the respective controllablecoupling mechanism is possible, and an uncoupled state, wherein thequbit does not capacitively affect the bus segment.

4. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a known bus architecture in accordance with the priorart.

FIG. 2A and FIG. 2B illustrate known bus architectures in accordancewith the prior art.

FIG. 3A and FIG. 3B illustrate mechanisms for coupling a qubit to asuperconducting bus in accordance with embodiments of the presentinvention.

FIG. 4 illustrates a bus architecture in accordance with an embodimentof the present invention.

FIG. 5A and FIG. 5B illustrate bus architectures in accordance with anembodiment of the present invention.

FIG. 6 illustrates a method for entangling or performing a couplingoperation between a first and second qubit in a quantum register inaccordance with an embodiment of the present invention.

FIG. 7 illustrates a method for performing a coupling operation betweena first and second qubit in a quantum register in accordance with anembodiment of the present invention.

FIG. 8 illustrates an apparatus that allows for the controlled couplingof qubits in a quantum register in accordance with an embodiment of thepresent invention.

FIG. 9A illustrates an embodiment of a qubit tree architecture inaccordance with one embodiment of the present invention

FIG. 9B illustrates an embodiment of the phase-charge qubit.

FIG. 9C illustrates an embodiment of a qubit tree architecture inaccordance with another embodiment of the present invention

Like reference numerals refer to corresponding parts throughout theseveral views of the drawings.

5. DETAILED DESCRIPTION

In accordance with the present invention, a scalable superconducting busarchitecture for quantum processing comprises a plurality of qubits,where all or a portion of the plurality of qubits are controllablycoupled to the bus. The size of the superconducting bus is limited onlyby its effective capacitance and the coherence length of the materialused to make the bus. This novel architecture provides three advantagesover the prior art. First, the effective-capacitance of thesuperconducting bus does not significantly depend on the number ofqubits that are coupled to the bus. Thus, the number of qubits that canbe coupled with the bus in the present invention is greater than thatfound in prior art systems. Second, there is no limitation to the energylevel spacing spectrum of the qubits as is the case for the resonantcontrolled qubit system (RCQS) described in Section 2.4 above, becausethe qubits can be controllably uncoupled from the superconducting bus ina reversible, controllable fashion. When a qubit is controllablyuncoupled from the bus, it does not substantially contribute to theeffective capacitance of the bus. Third, the energy spacing of therelevant energy levels of each of the qubits controllably coupled to thesuperconducting bus can be similar or identical, thereby simplifying thequantum architecture and making it cheaper to build.

In accordance with the present invention, when a qubit is coupled to asuperconducting bus, it is possible to controllably perform a couplingoperation on the qubit and bus by controlling the characteristics of thebus or the qubit, or both. The characteristics of the qubit can comprisethe energy-level spacing between the two lowest energy levels of thequbit, or the coupling strength between the qubit and the bus. Thecharacteristics of the bus can comprise the energy-level spacing betweenthe two lowest energy levels in a quantum device connected to the bus,the coupling strength between the qubit and the bus, or the state of acontrollable coupling device connected to the bus and qubit.Furthermore, when a qubit is uncoupled from a bus, the qubit and bus donot interact, although in some embodiments their states may remainentangled, and the characteristics (e.g., effective capacitance) of thebus are not substantially affected by the qubit.

5.1 Single Bus Architectures

One aspect of the present invention provides a novel bus architecturefor quantum processing. The architecture comprises a superconducting busand a plurality of qubits coupled to the bus. All or a portion of thequbits in the plurality of qubits are each respectively associated witha qubit controller that can be used to implement single qubitoperations. The architecture makes use of controllable couplingmechanisms to couple all or a portion of the qubits in the plurality ofqubits to the bus. Each such controllable coupling mechanism ischaracterized by (i) a first (coupled) state that allows the qubitconnected to the coupling mechanism to interact with the bus, thusallowing coupling operations to be performed on the qubit and bus, and(ii) a second (uncoupled) state in which the qubit is uncoupled from thebus. In the first (coupled) state, the bus is capable of interactingwith the quantum state of the qubit as well as mediating couplingoperations between the associated qubit and any other qubit coupled tothe bus. In the second (uncoupled) state, the associated qubit cannotinteract with the bus or any other qubits that are coupled to the bus.Only qubits that are coupled to a bus through a controllable couplingmechanism that is in a first (coupled) state (and optional qubits thatare directly capacitively coupled to the bus as described in Section2.4) contribute to the effective capacitance of the bus. Qubits that arecoupled to the bus through a controllable coupling mechanism in thesecond (uncoupled) state contribute zero or less than 1 attofarad to theeffective capacitance of the superconducting bus. In some embodiments,the bus is fabricated from a conventional superconducting material.Exemplary conventional superconducting materials include, but are notlimited to, aluminum, niobium, and lead. The buses are referred toherein as superconducting because they are fabricated from materialsthat, under certain conditions, can exist in a superconducting state.Such buses are still referred to as superconducting herein even whenthey are not in their superconducting state. However, it will beappreciated that quantum computation using the inventive architecturecan only take place when the superconducting bus is, in fact, in asuperconducting state.

A direct capacitive coupling between a qubit and a bus does notnecessarily allow coupling operations between the bus and the qubit.This property was exploited in the RCQS architecture described inSection 2.4 to allow for the selective coupling of qubits in a quantumregister. However, in the RCQS, the capacitive coupling between thequbits and the bus always contributes to the effective bus capacitance,regardless of whether the qubit is needed in a given quantum operation.This property necessarily limits the total number of qubits that can bepermanently coupled to the bus. Thus, rather than using a directcapacitive coupling between each qubit and the bus, the presentinvention uses controllable coupling mechanisms to controllably coupleall or a portion of a plurality of qubits to a bus. The use of thecontrollable coupling mechanism overcomes the limitation of excessivecapacitance because qubits coupled to the bus by controllable couplingmechanisms in the second (uncoupled) state contribute zero orsubstantially zero capacitance to the bus. Thus, in the presentinvention, more qubits can be coupled to the bus than in the RCQSarchitecture described in Section 2.4 without exceeding the capacitancethreshold of the bus that, once exceeded, precludes useful quantumcomputation. In typical operation, at any give time, only a subset ofthe controllably coupled qubits are in their first (coupled) state, sothat the capacitance threshold of the bus is not exceeded. For typicalarchitectures, C_(resonator)=5.8 pF, and C_(qubit)=5.5 fF. Qubits can beadded to the bus, so long as the total sum of the qubit capacitancesdoes not approach C_(resonator). In some embodiments, 10-100 qubits canbe added to the bus before the sum of the qubit capacitances approachesthe capacitance of the resonator and adversely affects the operation ofthe bus.

In some embodiments of the present invention, a mechanism forcontrollably coupling a qubit to a bus comprises a variableelectrostatic transformer (VET), such that in an uncoupled state the VETis tuned to have zero capacitance, and in a coupled state the VET istuned to have a finite capacitance appropriate for controllably couplingthe qubit with the bus.

FIG. 3A illustrates an embodiment of the present invention in which acontrollable coupling mechanism 320 controllably couples a qubit 360 anda bus 350. One mechanism for controllable coupling 320 comprises the useof an island 322 isolated by capacitors 323-1 and 323-2, a Josephsonjunction 321, and a gate voltage 324. In some embodiments, gate voltage324 is tuned to control the effective capacitance of controllablecoupling mechanism 320. In some embodiments, controllable couplingmechanism 320 has a first (coupled) state, such that the effectivecapacitance between qubit 360 and bus 350 is some finite value otherthan zero, and an uncoupled state, in which the effective capacitancebetween qubit 360 and bus 350 is zero or substantially zero. Theinteraction between qubit 360 and bus 350 is determined in part by theeffective bus capacitance of bus 350. The effective capacitance of thebus is, in turn, is determined by the physical size of bus 350 and bythe number of sources of capacitance (e.g., capacitance associated withqubits 360) attached to the bus. When controllable coupling mechanism320 is in the second (uncoupled) state, it provides zero orsubstantially zero effective capacitance to the effective capacitance ofbus 350. Hence, in some embodiments of the present invention, theeffective bus capacitance is a function of (i) the size of the bus and(ii) the number of controllable coupling mechanisms 320 coupled to thebus in a coupled state. In such embodiments, the effective buscapacitance is not a function of the number of qubits 360, per se, thatare coupled to the bus. Mechanisms 320 can be manufactured using knownlithographic and/or nanotechnology techniques.

Fabrication of mechanisms 320, qubits 360, bus 350 and other componentsof the present invention are well known in the art. Many of theprocesses for fabricating superconducting circuits are the same as, orsimilar to, those established for semiconductors. One important aspectof fabrication is the composition of the circuit. Niobium (Nb) andaluminum (Al) are superconducting materials common to superconductingcircuits. Less commonly used are superconducting materials such as lead,niobium (75%)-titanium (25%), and niobium-tin. Further, any of the 40 K(e.g., a 1-2-3 ceramic such as YBa₂Cu₃O_(6.9)) or the 95 Khigh-temperature superconductor materials can be used. See, for example,Hunt, 1989, Superconductivity Sourcebook, pp. 9-13, John-Wiley & Sons,New York. In some embodiments of the present invention, substantialportions of mechanisms 320 and qubits 360 are fabricated from niobium oraluminum. Insulating material, such as aluminum oxide or silicon oxide,is also used for the insulating gap in Josephson junctions. The processfor fabricating Josephson junctions is sometimes called a trilayerprocess, since a Josephson junction includes three distinct layers: abottom electrode, an insulating layer, and a top electrode. Theelectrodes are made from superconducting material. For example, thecomposition of a Josephson junction layer can be written asNb—AlO_(x)—Nb, where the Nb layers are the electrodes and AlO_(x)(aluminum oxide) is the insulating layer. In some embodiments of thepresent invention, the superconducting chip comprises niobium oraluminum circuits deposited on a silicon wafer. In some embodiments ofthe present invention, the superconducting chip comprises niobium oraluminum circuits deposited on oxidized silicon (SiO_(X)) disposed ontop of a silicon wafer. The depth of the oxidized silicon layer can beas little as several hundred nanometers.

The exact fabrication method used depends on the composition and size ofthe Josephson junction. For example, when fabricating large (e.g., 3×3μm²) Nb—AlO_(x)—Nb junctions according to one known fabricationapproach, the first step involves depositing a thin film of photoresistonto the wafer. The photoresist is then exposed using opticallithography to define the areas on the chip where the junctions willreside. The photoresist is then developed, causing the exposed areas tobe removed. Next, the niobium bottom electrode of the junction isdeposited by sputtering, followed by the deposition of a pure aluminumlayer that is also deposited by sputtering. This aluminum layer issubsequently oxidized to form the insulating material. The thickness ofthe insulating layer determines junction parameters, such as capacitanceand critical current density, and is usually between about a fewnanometers to several hundred nanometers. The top layer is thendeposited by sputtering. The sputtering of the junction layers isusually done at an angle normal to the wafer substrate. A lift-off isperformed, which etches away the remaining photoresist and any trilayerareas that formed on top of it, leaving behind only the areas, whichwere deposited in the developed photoresist regions. A secondphotoresist mask is used to expose certain areas and reactive ionetching is performed, which etches part of the top niobium electrodeaway, thereby defining the effective junction area. The sides of thejunction are electrically insulated by deposition of silicon oxide.Finally, another film of niobium is lithography deposited to connect thetop electrode to other circuitry. For more information, see Kohlstedt etal., 1993, IEEE Transactions on Applied Superconductivity 3, 2197; Yudaet al., 1987, Japan Journal of Applied Physics 26(3):L166; Wallraff,2000, Thesis, Friedrich-Alexander University of Erlangen-Nuremberg,Germany, pp. 20-21, each of which is hereby incorporated by reference inits entirety.

For smaller junctions, like submicron junctions, other techniques suchas shadow evaporation have been used. Submicron junctions are junctionsthat have at least one spatial dimension that is less than a micron insize. To illustrate, consider the fabrication of a small Al—Al₂O₃—AlJosephson junction. In one fabrication approach, first the silicon waferis cleaned and two resist layers are deposited on the substrate. Theupper resist layer is several tens of nanometers thick while the lowerresist layer is a few hundred nanometers thick and is more sensitive toelectrons. The device patterns are etched using an electron beamlithography technique. Afterwards, the resist is developed and etchedoff. Due to back-scattering of electrons and the greater sensitivity ofthe lower resist layer, a larger portion of the lower layer will beremoved relative to the upper layer, forming an undercut. The sample ismounted in an evaporator with a sample holder that is rotated anddouble-angle evaporation is performed. In double-angle evaporation, thebottom aluminum electrode is sputtered onto the wafer at an angle α.This is followed by deposition and oxidation of a thin insulating layer,and finally sputtering of the upper layer at an angle −α. The angleddeposition, combined with the undercutting of the resist, allows theformation of junctions with small dimensions. The process is finished bya lift-off, removing excess resist and trilayer depositions. Moreinformation on fabrication processes for small junctions can be found inDolan, 1977, Applied Physics Letters 31, 337; Majer, 2002, Thesis, DelftUniversity of Technology, pp. 12-13; Paauw, 2001, Thesis, DelftUniversity of Technology, pp. 34-36, 58-60; Born et al., 2001, IEEETransactions on Applied Superconductivity 11, 373; Koval et al., 1999,IEEE Transactions on Applied Superconductivity 9, 3957; and Fetter etal., 1983, U.S. Pat. No. 4,370,359, each of which is hereby incorporatedby reference in its entirety.

In some embodiments of the present invention, Josephson junction 321 isa submicron junction and double-angle evaporation is used to deposit thejunction layers. In some embodiments of the present invention, theJosephson junction is not submicron and the junction layers aresputtered at an angle normal to the wafer surface. In some embodimentsof the present invention, Josephson junction 321 has feature sizes thatare less than 2 microns and electron beam lithography is used to patternthe chip. In some embodiments of the present invention, Josephsonjunction 321 has feature sizes that are more than 2 microns andphotolithography is used to pattern the chip.

Furthermore, similar and alternative fabrication strategies aredescribed in Van Zant, 2000, Microchip Fabrication, McGraw-Hill, NewYork; Handbook of Microlithography, Micromachining, andMicrofabrication, Rai-Choudhury ed. 1997, The Society of Photo-OpticalInstrumentation Engineers, Bellingham, Wash.; Levinson, 2001, Principalsof Lithography, The Society of Photo-Optical Instrumentation Engineers,Bellingham, Wash.; and Madou, Fundamentals of Microfabrication, TheScience of Miniaturization, Second Edition, 2002, CRC Press LLC, BocaRaton, Fla., each of which is hereby incorporated by reference in itsentirety.

Capacitances between qubit 360 and bus 350 that are useful forperforming a coupling operation between the two components range fromabout 1 attofarad to about 1 nanofarad. As discussed in Section 5.4,below, examples of qubits 360 are phase qubits, charge qubits, andhybrid qubits. Moreover, combinations of any of these qubit types can beattached to bus 350 and used as a quantum register.

5.1.1 Controllable Coupling Mechanisms

An overview of inventive quantum computing architectures in accordancewith the present invention has been presented. Next, more details of acontrollable coupling mechanism will be described. Then, methods forcoupling a first qubit with a second qubit in a quantum register thatincludes the inventive architecture will be described.

Again referring to FIG. 3A, in one embodiment, controllable couplingmechanism 320 is a VET. See, for example, Averin and Bruder, 2003,“Variable Electrostatic Transformer Controllable Coupling of Two ChargeQubits,” Phys. Rev. Lett. 91, 57003, which is hereby incorporated byreference in its entirety. Conventional capacitive coupling of chargequbits permits the charge in a first cooper pair box (CPB) to interactwith the charge in a second CPB, which is coupled to the first CPB,resulting in always-on coupling and leading to a constraint inimplementing quantum computing algorithms. It is desirable to be able toswitch off such a coupling in some controllable way. To address theseconstraints, Averin and Bruder used a VET to provide a tunable couplingbetween two charge qubits, such as CPBs or Josephson charge qubits. TheVET proposed by Averin and Bruder separates charge qubits using atunable capacitance. Averin and Bruder demonstrated that the VET iscapable of being tuned to zero capacitance, hence removing theelectrostatic coupling between charge qubits.

In FIG. 3A, Josephson junction 321 is included roughly orthogonal to thecoupling direction defined by the junction of qubit 360 and bus 350 toisland 322. More specifically, this coupling direction is defined by thecapacitive coupling of qubit 360 and bus 350 to central island 322 oftransformer 320 through capacitances 323-1 and 323-2. Gate voltage 324is adjusted to achieve two states, a first (coupled) state in which bus350 and qubit 360 are capacitively coupled to each other and a second(uncoupled) state in which bus 350 and qubit 360 are not capacitivelycoupled to each other. Josephson junction 321 has dimensions rangingfrom about 0.001 square microns to about 1,000 square microns.Capacitances 323-1 and 323-2 have values ranging from about 1 attofaradto about 1 nanofarad. An example of a gate voltage in the first state is2.2 μV. An example of a gate voltage in the second state is 4 μV.However, these values are by way of illustration only and other valuesare possible.

5.1.2 Coupling Operations Using a Controlled Resonator

Referring to FIG. 3B, one aspect of the present invention provides acoupling operation between a first qubit 360 and a second qubit 360connected to a superconducting bus 350. A first and second controllablecoupling mechanism 320 that respectively couple the first and secondqubits 360 to bus 350 are in a first coupled state. In the operation,first and second qubits 360 are tuned to perform a coupling operationsuch that the quantum information stored in first and second qubits 360interact with bus 350 and hence with each other. In some embodiments, atuning operation comprises first tuning the characteristics of bus 350such that the quantum energy level separation associated with bus 350matches a quantum energy level separation associated with the firstqubit 360 for a first period of time. Then the characteristics of thebus are tuned such that the quantum energy level separation associatedwith bus 350 matches a quantum energy level difference associated withthe second qubit 360 for a second period of time. In some embodimentsthe first period of time and the second period of time eachindependently range between one picosecond and one millisecond. In otherwords, there is no requirement that the first period of time and thesecond period of time be the same.

In some embodiments, tuning the characteristics of the bus comprisesfirst tuning a quantum device (e.g., device 920) that is coupled to thebus. In some embodiments, tuning this quantum device comprises applyinga bias current (for example, in a CBJJ, applying a bias current between0.97 and 0.995 of the critical current of the Josephson junction)directly to the quantum device, or applying a gate voltage directly tothe quantum device. The exact gate voltage depends on thecharacteristics of the quantum device, such as capacitance values, butin some embodiments the applied gate voltage is between 1 nV and 1 μV,and in other embodiments the applied gate voltage is between 1 μV and 1V.

FIG. 6, with reference to the elements of FIG. 3B, illustrates a methodin accordance with this aspect of the invention. In step 6002,controllable coupling mechanisms 320 are in a default second (uncoupled)state so that qubits 360 connected to bus 350 by mechanisms 320 do notcontribute to the effective-capacitance of the bus. In step 6004, afirst controllable coupling mechanism 320 that controllably couples thefirst qubit 360 to bus 350 and a second controllable coupling mechanism320 that controllably couples the second qubit 360 to bus 350 are eachplaced in a first (coupled) state thereby coupling the first and secondqubits 360 to bus 350. There is no requirement in step 6004 that the twocontrollable coupling mechanisms be placed in the coupled state at thesame time. They can, for example, be sequentially placed in the coupledstate.

In step 6006, a resonant control system 920 (e.g., resonant controller920 of FIG. 1) that is coupled to bus 350 is biased to a first frequencyω₁₂ that represents the energy differential between a first quantumenergy level and a second quantum energy level (e.g., the lowest twoquantum energy levels) of first qubit 360 so that the quantum state ofresonant control system 920 couples with the quantum state of the firstqubit 360 via bus 350. The resonant control system 920 remains atfrequency ω₁₂ for a sufficiently long period of time for the resonantcontroller and the first qubit 360 to couple via bus 350.

In step 6008, resonant control system 920 is biased to a secondfrequency ω₃₄ that represents the energy differential between a firstquantum energy level and a second quantum energy level (e.g., the lowesttwo quantum energy levels) of second qubit 360 so that the quantum stateof the resonant control system 920 couples with the quantum state of thesecond qubit 360 via bus 350. The resonant control system 920 remains atfrequency ω₃₄ for a sufficiently long time for the resonant controlsystem 920 and the first qubit 360 to couple via bus 350. In the methodillustrated in FIG. 6, the first frequency ω₁₂ and the second frequencyω₃₄ are different.

Steps 6002-6008 allow for the coupling of any two qubits 360 coupled tobus 350. The limitation of the method illustrated in FIG. 6 is that thefirst and second qubits 350 must have unique energy differentials. Themethod illustrated in FIG. 7, with reference to the elements of FIG. 3B,circumvents this requirement.

In step 7002, controllable coupling mechanisms 320 are in a defaultsecond (uncoupled) state so that qubits 360 connected to bus 350 bymechanisms 320 do not contribute to the effective capacitance of thebus. In step 7004, a first controllable coupling mechanism 320 thatcontrollably couples first qubit 360 to bus 350 is placed in a first(coupled) state thereby coupling first qubit 360 to bus 350.

In step 7006, a resonant control system 920 (e.g., resonant controller920 of FIG. 3B) that is coupled to bus 350 is biased to a firstfrequency ω₁₂ that represents the energy differential between a firstquantum energy level and a second quantum energy level (e.g., the lowesttwo quantum energy levels) of first qubit 360 so that the quantum stateof the resonant control system 920 couples with the quantum state of thefirst qubit 360. The resonant control system 920 remains at firstfrequency ω₁₂ for a sufficiently long period of time for resonantcontrol system 920 and the first qubit 360 to couple. In someembodiments this time ranges between one picosecond and one millisecond.

In step 7008, the first controllable coupling mechanism 320 thatcontrollably couples the first qubit 360 to bus 350 is placed in asecond (uncoupled) state thereby capacitively decoupling first qubit 360from bus 350. In step 7010, the second controllable coupling mechanism320 that controllably couples second qubit 360 to bus 350 is placed in afirst (coupled) state thereby capacitively coupling the second qubit 360to bus 350.

In step 7012, the resonant control system 920 is biased to a secondfrequency ω₃₄ that represents the energy differential between a firstquantum energy level and a second quantum energy level (e.g., the lowesttwo quantum energy levels) of second qubit 360 so that the quantum stateof the resonant control system 920 couples with the quantum state of thesecond qubit 360. In the method illustrated in FIG. 7, frequencies ω₃₄and ω₁₂ can be the same or different. Resonant control system 920remains at second frequency ω₃₄ for a sufficiently long time for theresonant control system and the second qubit 360 to couple. In someembodiments this time ranges between one picosecond and one millisecond.

Values for the frequencies ω₁₂ and ω₃₄ depend on what kind of qubit isused, and also on the various characteristics of the qubits, such as thecharging energy E_(C) and the Josephson energy E_(J), which depend onthe physical parameters of the Josephson junctions. For quantroniumqubits, ω has a nominal value of about 16 GHz, but can range between 1and 50 GHz. For charge qubits, ω ranges between about 7 GHz and about 70GHz. For phase-charge qubits, ω has a nominal value of around 6.8 GHz,and ranges between about 1 and 100 GHz.

5.1.3 Other Single Bus Coupling Embodiments

In some embodiments of the present invention, characteristics (e.g.,gate charge) of the first and second qubits are tuned, such that thequantum information in one qubit interacts with the quantum informationin the second qubit through a controllable coupling mechanism 320. Insome embodiments, the apparatus, systems, and methods found in U.S.patent application Ser. No. 10/934,049, Sep. 3, 2004, entitled“Superconducting Phase-Charge Qubits,” hereby incorporated by referencein its entirety and referred to herein as Amin et al., are modified suchthat all or a portion of the qubits coupled to a superconducting bus arecoupled through a controllable coupling mechanism 320. FIG. 8illustrates.

In FIG. 8, a structure 8000 for controllably coupling and reading out aplurality of phase-charge qubits 8201 is provided. In some embodimentsin accordance with FIG. 8, element 320 is a controllable couplingmechanism that is equivalent to (same as) the controllable couplingmechanism illustrated in FIG. 3. Structure 8000 comprises a plurality ofN phase-charge qubits 8201, labeled from 8201-1 through 8201-N. Eachphase-charge qubit 8201 has one island capacitively coupled with a busisland 8550 through a controllable coupling mechanism 320. In Amin etal., each phase-charge qubit 8201 is directly coupled with bus island8550 through a capacitor. Thus, Amin et al. has the drawback that theeffective capacitance of bus island 8550 is a function of the number ofqubits coupled to the island. This significantly limits the number ofqubits that can be coupled to the bus island 8550 because of the buildup in the effective-capacitance of bus island 8550 as additional qubits8201 are added. As such, the present invention allows for significantlymore qubits to be added to each bus island 8550.

As in Amin et al., each phase-charge qubit 8201 has an islandcapacitively coupled to a readout apparatus 8230. Structure 8000additionally comprises gate voltages 8220-(2 i−1), where i is the qubitlabel in the range from 1 to N, that control the charge on thecorresponding qubit's readout island and gate voltage 8220-2 i thatcontrol the charge on the corresponding qubit's coupling island.

Amin et al. teaches a method for performing coupling operations betweena first phase-charge qubit 8201-L and a second phase-charge qubit8201-M, where L and M are independent integers between 1 and N, in whichgate voltages 8220-2L and 8220-2M that correspond to qubits 8201-L and8201-M are tuned such that the charge of the coupling islands on qubits8201-L and 8201-M depends on the quantum information contained in qubits8201-L and 8201-M, respectively. The qubits are maintained in this statefor a period of time such that a coupling operation is performed withthese qubits to completion. In some embodiments, this period of timeranges between one picosecond and one millisecond. Gate voltages 8220-I,where I represents each integer between 1 and 2N, other than theintegers 2L and 2M, are tuned so that the effective charge on thecoupling islands in qubits 8201-J where J represents each integerbetween 1 and N other than the integers L and M is small enough toprevent these qubits from interacting with bus island 8550. In someembodiments of the present invention, two or more phase-charge qubits8201 are coupled to bus island 8550 simultaneously using the methoddescribed above. In the present invention, the Amin et al. apparatus andmethods are enhanced by setting the respective controllable couplingmechanisms 320 corresponding to each qubit to be coupled to (i) a first(coupled) state during coupling operations and (ii) a second (uncoupled)state at all other times.

5.2 Bus and Pivot Segment Architectures

In another aspect of the present invention, a quantum processingarchitecture includes a plurality of superconducting buses, where eachsuperconducting bus forms a bus segment, one or more pivot segments, anda plurality of controllable coupling mechanisms for controllablycoupling a pivot segment to a bus segment. In some embodiments, thereare two or more buses, between two and twenty buses, more than tenbuses, or more than twenty buses. Each controllable coupling mechanismhas a first (coupled) state in which a controllable coupling operationbetween a bus segment, or a qubit in a bus segment, and a pivot segmentis possible. Further, each controllable coupling mechanism has a second(uncoupled) state in which the pivot segment does not capacitivelyaffect the bus segment. The pivot segments are used to control the flowof quantum information between bus segments. In some embodiments of thepresent invention, the requirements of each bus segment are reduced, ascompared with Blais et al., by using pivot segments to mediate quantumcoupling operations such as coupling operations. This further reducesthe number of required steps in realizing a coupling operation betweenqubits in different bus segments.

FIG. 4 illustrates a section of bus architecture 400 in accordance withan embodiment of the present invention. Bus architecture 400 includessuperconducting bus segments 350-N and 350-M separated by a pivotsegment 460-N, qubits 110-N1 through 110-NM connected to bus 350-Nthrough controllable coupling mechanisms 320-N1 through 320-NM, andqubits 110-M1 through 110-ML connected to bus segment 350-M throughcontrollable coupling mechanisms 320-M1 through 320-ML. Qubits 110 areeach associated with a respective qubit controller 112 and qubit device111, and are each connected to either bus segment 350-N or 350-M througha controllable coupling mechanism 320, such as the variableelectrostatic transformer (VET) illustrated in FIG. 3A. Eachcontrollable coupling mechanism 320 has a first (coupled) state,characterized by a finite nonzero capacitance, such that a couplingoperation between the corresponding qubit 110 and bus 350 is possible,and a second (uncoupled) state, characterized by a zero or substantiallyzero capacitance, whereby the corresponding qubit 110 does notcapacitively affect the corresponding bus segment 350 and qubit 110 isuncoupled from the bus segment.

Pivot segments 460 can be used to controllably perform couplingoperations between any qubit 110-N connected to bus 350-N and any qubit110-M connected to bus 350-M. Each pivot segment 460 is flanked by apair of controllable coupling mechanisms 461/462 as illustrated in FIG.4. Mechanisms 461/462 controllably couple a pivot segment 460 toadjoining bus segments 350. Further, each pivot segment 460 iscontrollably connected to a pivot device 464. Mechanisms 461/462 eachindependently have (i) a coupled state, such that a coupling operationis possible between a pivot segment 460 and an adjoining bus segment 350(or any qubit 110 coupled with the bus segment 350), and (ii) anuncoupled state, such that the state of pivot segment 460 does notaffect the respective adjoining bus segment 350.

In some embodiments, mechanisms 461 and 462 are each a VET 320 havingthe architecture illustrated for element 320 of FIG. 3. In someembodiments of the present invention, pivot device 464-N comprises aquantum device 474-N. In some embodiments, pivot device 464-N furthercomprises a mechanism 484-N for tuning the energy level separationbetween the respective energy levels or other characteristics of quantumdevice 474-N. In some embodiments, pivot device 464-N is the same asqubits 110, that is, quantum device 474-N is the same as qubit device111 and tuning mechanism 484-N is the same as tuning mechanisms 112.

In some embodiments, tuning mechanism 112 and/or 484 comprises anycombination of a current source, a voltage source, and a flux source.Each such source is capable of controlling some aspect of the state ofthe corresponding qubit 110 and/or pivot device 464. Examples of qubits110 and/or pivot device 464 useful for the present invention include,but are not limited to, current biased Josephson junction (CBJJ) qubits,phase-charge qubits, quantronium qubits, and charge qubits. See Makhlinet al., 2001, “Quantum-State Engineering with Josephson-JunctionDevices,” Rev. of Mod. Phys., 73, pp. 357-401, which is herebyincorporated by reference in its entirety, for more description of suchqubits 110 and/or 464.

Referring to FIG. 4, when mechanism 461-N is in a coupled (closed)state, a coupling operation is possible between bus segment 350-N andpivot segment 460-N. Typically, pivot segment 460 is either uncoupledfrom all bus segments or is coupled to a single bus segment at any giventime when device 400 is being used to perform quantum computations.

An aspect of the present invention provides methods for using a pivotsegment 460 to perform one or more coupling operations on a first qubit110-N from a first bus segment 350-N and a second qubit 110-M from asecond bus segment 350-M in an architecture 400 such as that disclosedin FIG. 4. The pivot segment 460 is controllably coupled to the firstbus segment 350-N by a first controllable coupling mechanism 461, and iscontrollably coupled to the second bus segment 350-M by a secondcontrollable coupling mechanism 462. The first qubit 110-N iscontrollably coupled to the first bus segment 350-N by a first qubitcontrollable coupling mechanism 320-N. The second qubit 110-M iscontrollably coupled to the second bus segment 350-M by a secondcontrollable coupling mechanism 320-M. In one method in accordance withthis aspect of the invention, the first controllable coupling mechanism461 is adjusted from a default uncoupled state to a coupled state,thereby coupling the pivot segment 460 to the first bus segment 350-N.The corresponding first qubit coupling mechanism 320-N is also set to acoupled state, thereby capacitively coupling the first qubit 110-N tothe first bus segment 350-N as well. A first coupling operation betweenthe first qubit 110-N and the pivot segment 460 is performed. Then, thefirst controllable coupling mechanism 461 and the first qubitcontrollable coupling mechanism 320-N are placed into an uncoupled(open) state, thereby capacitively (and quantum mechanically) isolatingthe first qubit 110-N and the pivot segment 460 from first bus segment350-N and thereby decoupling first qubit 110-N and pivot segment 460.Next or simultaneously, the second controllable coupling mechanism 462is set from a default uncoupled state to a coupled state, therebycapacitively coupling pivot segment 460 with second bus segment 350-M.Also, second controllable coupling mechanism 320-M is set from anuncoupled state to a coupled state, thereby capacitively coupling thesecond qubit 110-M to the second bus segment 350-M as well. A secondcoupling operation is performed between pivot segment 460 and secondqubit 110-M. Then second controllable coupling mechanism 462 and secondcontrollable coupling mechanism 320-M are set to an uncoupled state,thereby capacitively (and quantum mechanically) isolating qubit 110-Mand pivot segment 460 from second bus segment 350-M.

In some embodiments of the invention, after performing the first andsecond coupling operations, first qubit 110-N, quantum device 474-N, andsecond qubit 110-M are in an entangled state even though they are nolonger coupled to each other. In some embodiments, a coupling operationbetween first qubit 110-N and second qubit 110-M further comprisesunentangling quantum device 474-N This extra step is needed, forexample, when performing a square root swap (√{square root over (SWAP)})gate operation. Such a √{square root over (SWAP)} operation is describedin Blais et al., 2003, Phys. Rev. Lett. 90, P. 127901, which is herebyincorporated by reference in its entirety.

In one embodiment, quantum device 474-N is unentangled by setting firstcontrollable coupling mechanism 461 and first qubit controllablecoupling mechanism 320-N to coupled states, thereby re-coupling pivotsegment 460 to first qubit 110-N. A third coupling operation (in thiscase, more precisely, an unentangling operation) is performed betweenpivot segment 460 and first qubit 110-N. Then the first controllablecoupling mechanism 461 and the first qubit controllable couplingmechanism 320-N are reset to the uncoupled state. After this thirdoperation, the quantum device 474-N is not entangled with first qubit110-N or second qubit 110-M.

In another such embodiment, quantum device 474-N is unentangled bysetting second controllable coupling mechanism 461 and second qubitcontrollable coupling mechanism 320-M to coupled states, therebyre-coupling pivot segment 460 to second qubit 110-M. A third quantumgate operation (in this case, more precisely, an unentangling operation)is performed between pivot segment 460 and second qubit 110-M. Then thesecond controllable coupling mechanism 461 and the second qubitcontrollable coupling mechanism 320-M are reset to the uncoupled state.After this third operation, the quantum device 474-N is not entangledwith the first qubit 110-N or second qubit 110-M.

The aforementioned first, second, and third operations can be performedin accordance with the methods described in U.S. patent application Ser.No. 10/419,024, filed May 17, 2003, entitled “Resonant Controlled QubitSystem,” as well as U.S. patent application Ser. Nos. 10/798,737,10/801,335, and 10/801,340 each of which are hereby incorporated byreference in its entirety.

In some embodiments of the present invention, the first, second, andthird coupling operations are performed by tuning pivot device 464-N(for example, this may be another qubit, or it may be resonator 920 orFIG. 2) attached to pivot segment 460-N to have an energy level spacingcorresponding to the energy level spacing of the qubit to which it iscoupled in any given coupling operation. For example, in the firstcoupling operation, the pivot segment 460-N is tuned to resonate at thefrequency corresponding to the energy spacing between a first and secondenergy level in the first qubit 110-N.

In some embodiments of the present invention, each pivot device 464 doesnot require a mechanism for tuning its state. In other words, in someembodiments, there is no requirement that each bus segment have a tuningdevice, such as tuning device 484-N of FIG. 4. In some embodiments, thepivot segment plays the role of mediating the coupling operation. Forexample, the energy level separation or other characteristics of quantumdevice 474 of pivot device 464 can be tuned to mediate a couplingoperation with the respective qubit. This further reduces therequirements for each bus segment, as well as the number of operationsrequired to implement a coupling operation between qubits in differentbus segments.

Another embodiment of the present invention provides a method forentangling or performing coupling operations between phase-charge qubitsusing an architecture similar to that of FIG. 4. In the method, thepivot segment is used to perform coupling operations between a firstqubit from a first bus segment and a second qubit from a second bussegment without any requirement for a tunable bus mechanism. The firstand second qubits are phase-charge qubits. The pivot segment is coupledto a quantum device. The pivot segment can be coupled with aphase-charge qubit such that coupling operations can be performed onthem. In the method, a first controllable coupling mechanism between thefirst phase-charge qubit and the first bus segment is placed into acoupled state. A second controllable coupling mechanism between thefirst bus segment and the pivot segment is placed into a coupled statethereby controllably coupling the first bus segment and the pivotsegment. A first coupling operation is performed by tuning the firstphase-charge qubit and the quantum device coupled to the pivot segmentto a charge-sensitive state for a first duration. Then the first andsecond controllable coupling mechanisms are placed into an uncoupledstate thereby decoupling the first phase-charge qubit and the quantumdevice.

A third mechanism for controllable coupling, which is between the pivotsegment and the second bus segment, is placed into a coupled state. Afourth controllable coupling mechanism that controllably couples thesecond bus segment to the second phase-charge qubit is placed into acoupled state. A second coupling operation is performed by tuning thesecond phase-charge qubit and the quantum device coupled to the pivotsegment to a charge-sensitive state for a second duration. In this way acoupling operation has been performed on the first and second qubits.The third and fourth controllable coupling mechanisms are then placedinto an uncoupled state.

In some embodiments of the invention, the method further comprises againplacing the first and second controllable coupling mechanisms into acoupled state, using the above-described steps. A third quantum couplingoperation is then performed by tuning the first phase-charge qubit andthe quantum device coupled to the pivot segment to a charge-sensitivestate for a third duration, causing the pivot segment to becomeunentangled from the first and second qubits. In an alternativeembodiment, the third and fourth controllable coupling mechanisms areagain placed in their coupled states and a third coupling operation isperformed by tuning the second phase-charge qubit and the quantum devicecoupled to the pivot segment to a charge-sensitive state for a thirdduration, which causes the pivot segment to become unentangled from thefirst and second qubits.

In some embodiments of the present invention, tuning a phase-chargequbit to a charge-sensitive state comprises applying a gate voltage tothe portion of the phase-charge qubit that is coupled to a bus segmentor to the mechanism for controllable coupling and setting the gatevoltage to a predetermined value. This gate voltage is predeterminedsuch that the charge on the islands has a certain value. For certainvalues of the charge on the islands the phase-charge qubit is decoupledfrom the bus segment, and for certain values of the charge on theislands, the phase-charge qubit is coupled to the bus segment. Detailedmethods for manipulating the phase-charge qubit are described in Amin etal. In some embodiments of the present invention, the quantum devicecoupled to the pivot segment is also a phase-charge qubit.

5.2.1 Multidimensional Qubit Coupling Architectures

FIG. 5A and FIG. 5B illustrate additional embodiments of the presentinvention.

In such embodiments, a bus architecture comprises a plurality of rows ofbus segments.

Each row comprises a plurality of bus segments and one or more pivotsegments. In some embodiments of the invention, a pivot segment iscapable of performing a coupling operation between bus segments in a rowor between bus segments in different rows.

FIG. 5A illustrates a portion 500 of a two-dimensional bus architecturecomprising N rows by M rows that includes a pivot segment 460-K. Eachrow, 350-1 through 350-N, comprises a plurality of bus segments 350 andeach bus segment 350 is connected to a plurality of qubits 110. Pivotsegment 460-K comprises quantum device 464-K−1 and, optionally, couplingelement 464-K−2. Pivot segment 460-K further comprises mechanisms forcontrollable coupling 461 and 462 for coupling pivot segment 460-K tobus segments 350. The two-dimensional bus architecture of FIG. 5A can beextended into a third dimension in which there are successive layers ofarchitecture 500, each layer controllably connected to the other by viasextending from, for example, positions 502 of architecture 500. In otherembodiments, such vias are positioned at other locations within pivotsegment 460-K. In still other embodiments, not every row 350 includes avia. In fact, in one embodiment, there is only one via in all of pivotsegment 460-K. In some embodiments, these vias are bordered bycontrollable coupling mechanisms (not shown) so that individual layers500 can be controllably coupled to each other. In this way, any qubit ina three-dimensional qubit array can be coupled with any other qubit inthe three dimensional qubit array using the methods described in thecase of a one-dimensional array described above.

FIG. 5B illustrates an embodiment of the present invention comprising aplurality of pivot segments 460 and a plurality of bus segments 350.Pivot segments 460 further comprise controllable pivot segment couplingmechanisms 569 for coupling a first subsegment of a pivot segment 460 toa second subsegment of a pivot segment 460. In some embodiments of theinvention, controllable coupling mechanism 569 allows intermediatecoupling operations to be performed between subsegments of pivot segment460. Each subsegment of pivot segment 460 comprises a quantum device464-K to mediate coupling operations between qubits as described above.In some embodiments of the present invention, each subsegment of pivotsegment 460 is in electrical communication with a controllable couplingmechanism 569 to controllably couple the subsegment to at least one bussegment such that each subsegment is capable of coupling to differentbus segments.

In accordance with the present invention, a coupling operation can beperformed between any first and second qubit in bus architecture 500 ofFIG. 5B by sequencing a series of steps passing through the appropriatepivot segments 460. The two-dimensional bus architecture of FIG. 5B canbe extended into a third dimension in which there are successive layersof architecture 500, each layer controllably connected to the other byvias extending from positions 502 of architecture 500. In someembodiments, these vias are bordered by controllable coupling mechanisms(not shown) so that individual layers 500 can be controllably coupled toeach other. As in the case of architecture 500 of FIG. 5A, in FIG. 5Bthere is no requirement for any via, and when vias are present in orderto couple one or more two-dimensional layers, such vias can be placed ineach row 350, on a portion (some) of the rows 350, or on a single row350. In this way, any qubit in a three-dimensional qubit array can becoupled with any other qubit in the three dimensional qubit array.

5.3 Tree Architectures

As indicated in the background section, scalability is an issue in thedevelopment of useful quantum computers. As the number of qubits scale,so does the complexity of the system. In linear bus type architectureslike those shown in FIG. 4, the qubits are arranged in a line and arecoupled either to nearest neighbors or to a common coupling bus. In thecase of nearest neighbor coupling, a swap between the end qubits of an Nqubit linear array takes N swap operations. In the case of bus couplingas in FIG. 4 with N buses 350, a swap operation between a qubit in thefirst bus and another qubit in the N^(th) bus takes N couplingoperations. In addition, the capacitance of the bus increases with thenumber of qubits coupled to it, thereby limiting the ability of the busto support quantum calculations.

In the case of two-dimensional qubit or three-dimensional lattices likethose shown in FIG. 5A and FIG. 5B, in the worst case, coupling betweentwo qubits takes √{square root over (N)} operations within a giventwo-dimensional layer. Thus, the two-dimensional and three-dimensionalqubit lattices of the present invention present a significantadvancement over linear bus architectures.

In an embodiment of the present invention, the qubits and couplingsystems are arranged as a tree, such as tree 900 that is illustrated inFIG. 9A. The root of tree 900, node 905-1, and all subsequent nodes905-2, 905-3, etc., branch off into two or more nodes. Two-nodebranching, where each parent node has two daughter nodes, is a preferredtree embodiment in accordance with the present invention, since such anarrangement minimizes capacitance of the bus lines between each of thenodes. In other embodiments, each parent node can have more than twodaughter nodes attached to it. In some embodiments, each parent node hask daughter nodes, where k is an integer in the set of 3 to 10,inclusive. In some embodiments, each parent node has the same or adifferent number of daughter nodes. Each parent node need not have thesame number of daughter nodes. In one embodiment, the root 901 level oftree 900 is a charge coupling system, like the resonant controlled qubitsystem of FIG. 1, for example. The next level, 902, contains nodes905-2, which are qubits, and level 903 contains nodes 905-3 which arecoupling systems. Levels of qubits and coupling systems continue toalternate in this fashion throughout the remaining lower levels 904 oftree 900 in this particular embodiment. However the root should be acoupling system while the lowest level of the tree should containqubits. In some embodiments each tree contains a minimum of three levelsup to a maximum of five or six levels.

In other embodiments of tree 900, nodes 905 in two or more adjacentlevels (e.g., levels 902 and 903) are qubits. In such embodiments, a VET320, switch 461/462, or other similar devices are used to controllablyisolate each of the nodes 905 in order to turn coupling to such qubitson or off. For example, a VET 320, switch 461/462, or other similardevice is placed between 905-2-1 and each of its daughter nodes (e.g.,between 905-2-1 and 905-3-1 as well as between 905-2-1 and 905-3-2). Inthis way, node 905-3-2 can be controllably decoupled from node 905-2-1while node 905-3-1 is coupled to node 905-2-1, and node 905-3-1 can becontrollably decoupled from node 905-2-1 while node 905-3-2 is coupledto node 905-2-1. In the case where a qubit has more than one couplingline and the coupling is controlled by the qubit itself, the device isnot needed. An example of this is the phase-charge qubit (PCQ).Referring to FIG. 9B, the phase-charge qubit has two couplingcapacitors, 916-1 and 916-2, each of which can be coupled to a couplingcapacitor 916 on another phase-charge qubit. The phase-charge qubit alsohas the ability to completely decouple itself from other qubits bytuning a gate voltage through mechanisms 915. Therefore, an additionalcontrollable coupling device such as a VET 320, switch 461/462, or othersimilar device is not needed to couple a phase-charge qubit to two otherphase charge qubits. In order for the phase-charge qubit to couple tomore than two daughter qubits, controllable coupling devices can beused.

FIG. 9B shows an embodiment of a phase-charge qubit 913. Quantumoperations are done in the phase regime, while initialization, readout,and coupling is done in the charge regime. Qubit 913 is asuperconducting loop interrupted by three Josephson junctions 911-1 to911-3. In some embodiments of the present invention the Josephson energyfor junctions 911 is 0.22 meV. In some embodiments of the presentinvention the Josephson energy for junctions 911 is between 0.22 meV and0.5 meV, and in some embodiments it is less than 0.22 meV. The threejunctions 911 define three superconducting islands. One island isgrounded, while the other two are capacitively coupled to mechanisms915. In some embodiments, capacitors 915-1-1 and 915-2-1 each have acapacitance of about 1 attofarad. In some embodiments, capacitors915-1-1 and 915-2-1 each independently have a capacitance between 1 zFand 1 pF. Mechanisms 915 are connected to a gate voltage to controlcoupling to other qubits via coupling capacitors 916. In someembodiments, each coupling capacitor 916 has a capacitance of about 1attofarad. In some embodiments, each coupling capacitor 916 has acapacitance between 1 zF and 1 pF. In addition, one or more mechanisms915 can initialize qubit 913 using a gate voltage. In some embodimentsthis gate voltage is between 1 pV and 1 V. One of mechanisms 915 canalso comprise a measurement device coupled to qubit 913. Such ameasurement device measures the charge of the island to which it iscoupled, and embodiments can include electrometers like the rf-SET.Mechanism 914 is used to inductively bias the flux of the qubit. In someembodiments, the mutual inductance of qubit 913 and mechanism 914 isbetween 0.1 pH and 100 pH.

In another embodiment of the phase-charge qubit, the superconductingloop is interrupted by four Josephson junctions, thereby forming fourislands. One island is grounded, while another island is capacitivelycoupled to a measurement device. The remaining two islands arecapacitively coupled to gate voltages that can control coupling and/orinitialize the system. Those two islands will also be in electricalcommunication with capacitors, thereby allowing the two islands to beconnected and coupled to other qubits. Such capacitors can have acapacitance in the range of 1 zF to 1 pF.

FIG. 9C shows an embodiment of a tree architecture 910 using qubits 913of FIG. 9B. Qubits 913 are not drawn out fully in FIG. 9C, but each is aqubit 913 of FIG. 9B described above. Root qubit 911-1 is connected totwo qubits 911-2-1 and 911-2-2 via coupling capacitors 912. In someembodiments coupling capacitors 912 are between 1 zf and 1 pF.Capacitors 912 can be fixed or variable in value. Each such branchingqubit is then connected to two more qubits, and so on, in order to formtree 910 of FIG. 9C.

To couple two qubits that are directly connected in the tree, theappropriate coupling voltages are tuned through mechanisms 915 for aperiod of time while all neighboring coupling voltages remain at zero.In some embodiments, the period of time is between one picosecond andone millisecond. To couple two qubits that are not directly connected, acoupling path is traced between the two qubits using other qubits. Forinstance, to couple qubits 911-2-1 and 911-2-2 in FIG. 9C, both can becoupled to qubit 911-1.

Each bus segment in a tree can have a small number of qubits connectedto it (between 2 and 10) and thus the overall capacitance of the systemremains low. Due to the tree-branching nature of the architectures shownin FIG. 9A and FIG. 9C, swapping two qubits takes log(N) couplingoperations in the worst case. In some embodiments, a tree architecturequbit circuit is implemented in a structure fabricated using niobium oraluminum superconducting material using known microfabricationtechniques. Referring to FIGS. 9A and 9C, in some embodiments controlwires (buses) are routed on layers above the circuit, and are connectedto nodes 905 through vias, which pass vertically through the layers inthe fabricated structure.

5.4 Qubits that Can Be Coupled Using the Inventive Architecture

Examples of superconducting qubits 110, 360, 464, 464-K, 610, and/or 905useful in the present invention include CBJJ qubits, charge qubits,phase-charge qubits, and charge-phase qubits (also known as quantroniumqubits). Quantronium and phase-charge qubits are respectively describedin U.S. patent application Ser. No. 10/244,634, filed Sep. 16, 2002,entitled “Superconducting quantum-bit device based on Josephsonjunctions”; and U.S. patent application Ser. No. 10/934,049, Sep. 3,2004, entitled “Superconducting Phase-Charge Qubits,” each of which ishereby incorporated by reference in its entirety. This section providesa description of qubits and then provides more details of exemplaryqubits that can be used in accordance with the present invention.

5.4.1 Qubit Properties

A quantum bit or “qubit” 110, 360, 464, 464-K, 610, and/or 905 is thebuilding block of a quantum computer in the same way that a conventionalbinary bit is a building block of a classical computer. A qubit is aquantum bit, the counterpart in quantum computing to the binary digit orbit of classical computing. Just as a bit is the basic unit ofinformation in a classical computer, a qubit basis state is the basicunit of information in a quantum computer. A qubit is conventionally asystem having many discrete energy states, the two lowest of which areused for normal operation of the qubit. The energy eigenstates of aqubit are generally referred to as the basis states of the qubit. Thelogical basis states of a qubit are termed the |0

and |1

basis states representing the ground and first-excited energy states ofthe qubit.

A qubit can be in any superposition of its basis states, making itfundamentally different from a bit in an ordinary digital computer. Asuperposition of basis states arises in a qubit when there is a non-zeroprobability that the system occupies more than one of the basis statesat a given time. Qualitatively, a superposition of basis states meansthat the qubit can be in both basis states |0

and |1

at the same time. Mathematically, a superposition of basis states meansthat the overall state of the qubit, which is denoted |ψ

, has the form|ψ

=a|0

+b|1

  (2)where a and b are probability amplitudes respectively corresponding toprobabilities |a|² of being in the |0

basis state and |b|² of being in the |1

state. The relationship|a| ² +|b| ²=1  (3)is satisfied by a qubit. The probability amplitudes a and b each havereal and imaginary components, which allows the phase of the qubit to bemodeled. The quantum nature of a qubit is largely derived from itsability to exist in a superposition of basis states.

To complete a computation using a qubit, the state of the qubit ismeasured (e.g., read out). When the state of the qubit is measured, thequantum nature of the qubit is temporarily lost and the superposition ofbasis states collapses to either the |0

or |1

basis state, thus regaining its similarity to a conventional bit. Theactual state of the qubit after it has collapsed depends on theprobability amplitudes a and b immediately prior to the readoutoperation.

A survey of the current physical systems from which qubits can be formedis Braunstein and Lo (eds.), 2001, Scalable Quantum Computers, Wiley-VCHVerlag GmbH, Berlin, which is hereby incorporated by reference in itsentirety. Of the various physical systems surveyed, the systems thatappear to be most suited for scaling (e.g., combined in such a mannerthat they interact with each other) are those physical systems thatinclude superconducting structures such as superconducting qubits.

5.4.2 Superconducting Qubits

One class of qubits is superconducting qubits. Superconducting qubitsgenerally have properties that fall into two categories; phase qubitsand charge qubits. Phase qubits are those that store and manipulateinformation in the phase states of the device. In other words, phasequbits use phase as the information-bearing degree of freedom. Chargequbits store and manipulate information in the charge states of thedevice. In other words, charge qubits use charge as theinformation-bearing degree of freedom. When superconducting materialsare cooled below a certain critical temperature, the free electronscondense and pair off with other electrons to form Cooper pairs. Thecollection of Cooper pairs in the material form a single condensate witha phase. Cooper pairs become the elementary charge carriers and eachCooper pair has a phase that is defined by the overall condensate. Thedivision of superconducting qubits into two classes is outlined inMakhlin et al., 2001, “Quantum-State Engineering with Josephson-JunctionDevices,” Rev. Mod. Phys. 73, pp. 357-401, which is hereby incorporatedby reference in its entirety.

Phase and charge are conjugate quantum variables in superconductors atenergy scales where quantum effects dominate. Phase qubits havewell-defined phase states for storing quantum information, and chargequbits have well-defined charge states for storing quantum information.

Experimental realization of superconducting devices as qubits was madeby Nakamura et al., 1999, Nature 398, pp. 786-788, which is herebyincorporated by reference. Nakamura et al. developed a charge qubit thatdemonstrates the basic operational requirements for a qubit, but withpoor (short) decoherence times and stringent control parameters.

Superconducting qubits have two modes of operation related tolocalization of the states in which information is stored. When thequbit is initialized or measured, the information is classical, 0 or 1,and the states representing that classical information must also beclassical in order to provide the most reliable state preparation. Somequbits, however, are not initialized in a classical state, but in aquantum superposition of states. Thus, a first mode of operation of aqubit is to permit state preparation and measurement of classicalinformation. A second mode of operation occurs during quantumcomputation, where the information states of the device become dominatedby quantum effects such that the qubit can evolve controllably as acoherent superposition of those states and, in some instances, becomecoupled and/or entangled with other qubits in the quantum computer.

Charge Qubit

A charge qubit comprises a Cooper pair box (CPB) isolated by one or twoJosephson junctions, and at least two capacitive gates, such that avoltage can be applied to the CPB and such that the charge of the CPB ismeasurable. The state of the charge qubit is based on the number ofCooper pairs in the CPB. The basis states |0

and |1

are typically respectively represented by n and n+1 Cooper pairs. Workhas demonstrated that it is possible to achieve ninety percentefficiency in detection of the state of the charge qubit. Charge qubitscan be coupled together through a capacitance. See e.g., Pashkin et al.,2003, Nature 421, pp. 823-826, which is hereby incorporated by referencein its entirety. Furthermore, simple quantum operations have beenperformed between two charge qubits that share a capacitive coupling.See e.g., Yamamoto et al., 2003, Nature, 425, pp. 941-944, which ishereby incorporated by reference in its entirety.

Phase Qubit

The current biased Josephson Junction (CBJJ) qubit is an example of aphase qubit. See, e.g., Martinis et al., “Rabi oscillations in a largeJosephson junction qubit,” preprint presented at the American PhysicalSociety (APS) 2002 Annual Meeting, held Jul. 27-31, 2002; and Han etal., 2001, Science 293, pp. 1457-1459, each of which is herebyincorporated by reference in its entirety. Some CBJJ qubits havedimensions of about 10 microns. Under the influence of a bias currentthat approaches the critical current of the junction, the potentialenergy of the CBJJ qubit forms a tilted washboard potential, havingperiodic minima with respect to the phase difference across thejunction. The basis states |0

and |1

of the CBJJ are typically the ground state and first excited energylevels in the potential minima. In order to perform quantumcomputations, the basis states of the CBJJ are allowed to evolve inaccordance with quantum mechanical principles. The state of the CBJJ canbe a superposition of these states and controlled quantum evolution ofthe CBJJ can be achieved by application of microwave frequency waves,current biasing, and entanglement of the quantum state of the CBJJ withthe quantum state of other qubits. Two or more CBJJs can be coupledcapacitively either directly or through a bus configuration. See e.g.,Blais et al., as well as Berkley et al., 2003, Science 300, pp.1548-1550, each of which is hereby incorporated by reference in itsentirety.

The observation of a state-dependent voltage across the CBJJ is acentral aspect to reading out the state of a CBJJ. In some embodiments,this state-dependent voltage ranges between 1 pV and 1 V. Typically,readout of the CBJJ is realized by applying a microwave frequency wave,such that the CBJJ is conditionally excited to a higher energy level.The frequency of this microwave frequency wave corresponds to the energydifferential between the higher energy level of the CBJJ and the lowerenergy level of the CBJJ that are used in a quantum computation. Thehigher energy level has a higher probability of escaping from thepotential well, resulting in a time-varying phase difference across theJosephson junction and a corresponding state-dependent voltage dropacross the CBJJ. A detrimental consequence of measurement of thisvoltage is that the CBJJ reaches an excited state resulting in thegeneration of thermal energy. Thus, the CBJJ qubit must be allowed somerelaxation time before being re-initialized in order to allow the heatto dissipate.

Hybrid Qubits

Charge qubit with phase control (quantronium). An exemplary hybrid qubitoperates using both phase and charge to store, manipulate, and readoutinformation. This qubit, variously called the Saclay qubit orquantronium, has a structure similar to a conventional charge qubitmodified to be read out in the phase regime. The quantronium qubit hasone degree of freedom in the phase basis and another degree of freedomin the charge basis. Readout of the quantronium involves measuring thephase of the hybrid qubit, but computation can involve interaction witheither the charge or phase degrees of freedom. See, for example, U.S.Pat. No. 6,838,694 B2, entitled “Superconducting quantum-bit devicebased on Josephson junctions,” as well as Vion et al., cited hereinabove, each of which is hereby incorporated by reference in itsentirety. The quantronium comprises a small superconducting island,playing the role of the Cooper pair box in the charge qubit, isolated bytwo Josephson junctions through which a bias current can interact withthe phase of the qubit, and gate voltages, through which the charge ofthe qubit can be controlled or detected.

Measurement of the quantronium, see e.g. Vion et al., comprises placinga large Josephson junction in a loop with the island and driving acurrent across the large Josephson junction. Under the influence of abias current, the qubit island develops a state-dependent current thatincreases or decreases the bias current across the large Josephsonjunction. Thus, depending on the state of the qubit, the large Josephsonjunction will enter the voltage state and the voltage can be detected inorder to confirm the state of the qubit. The quantronium can becapacitively coupled to other qubits either directly or by a busmechanism (see Blais et al.).

Phase-charge qubit. Another type of hybrid superconducting qubitexploiting charge control is the phase-charge qubit. The phase-chargequbit is presented in Amin et al. The structure of the phase-chargequbit is similar to that of a superconducting phase qubit including asuperconducting loop and a plurality of Josephson junctions forming aplurality of islands within the superconducting loop. The qubit furtherincludes gates for controlling the qubit state. The phase-charge qubitcan be controllably tuned to the charge basis, where the charge degreeof freedom depends on the quantum information stored in the qubit andcan be manipulated or detected.

Measurement of the phase-charge qubit comprises applying a gate voltage(e.g., 1 pV to 1 V) to one of the islands in the plurality of islandsand setting the gate voltage to a predetermined value. The gate voltageis different depending on the exact qubit being used, but it isdetermined based on what voltage is necessary to achieve a certaincharge on an island that is being coupled to a readout device. In someembodiments this voltage is such that the gate charge on a first islandcoupled to the readout device is n=¼ and the voltage on a second islandis such that the gate charge on the second island is n=0. Measurement ofthe phase-charge qubit comprises applying these voltages and detecting acharge on the first island. Capacitive coupling between phase-chargequbits can be achieved by applying a gate voltage to make one or moreislands of each phase-charge qubit sensitive to charge. In someinstances, this comprises applying a voltage such that the gate chargeon an island is n=¼ and n=0 on another island. Once tuned such that theresulting charges are state-dependent, the qubits can interactcapacitively with each other, hence entangling the states of the qubits.Tuning the phase-charge qubit, as described, is a quantum coherentoperation.

5.5 Cited References

All references cited herein are incorporated herein by reference intheir entirety and for all purposes to the same extent as if eachindividual publication, patent, patent application, or patentpublication was specifically and individually indicated to beincorporated by reference in its entirety for all purposes.

5.6 Conclusion

When introducing elements of the present invention or the embodiment(s)thereof, the articles “a,” “an,” “the,” and “said” are intended to meanthat there are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and to mean thatthere may be additional elements other than the listed elements.Moreover, the term “about” has been used to describe specificparameters. In many instances, specific ranges for the term “about” havebeen provided. However, when no specific range has been provided for aparticular usage of the term “about” herein, than either of twodefinitions can be used. In the first definition, the term “about” isthe typical range of values about the stated value that one of skill inthe art would expect for the physical parameter represented by thestated value. For example, a typical range of values about a specifiedvalue can be defined as the typical error that would be expected inmeasuring or observing the physical parameter that the specified valuerepresents. In the second definition of about, the term “about” meansthe stated value ±0.10 of the stated value.

While the present invention has been described with reference tospecific embodiments, the description is illustrative of the inventionand is not to be construed as limiting the invention. Variousmodifications may occur to those skilled in the art without departingfrom the true spirit and scope of the invention as defined by theappended claims. This patent specification concludes with the appendedclaims.

1. A quantum processing apparatus comprising: a superconducting qubit; asuperconducting bus; a quantum device coupled to the superconductingbus; and a controllable coupling mechanism that controllably couples thesuperconducting bus to the superconducting qubit, the controllablecoupling mechanism capable of being in any one of a plurality of statesat any given time, said plurality of states comprising: a first state inwhich the superconducting bus and the superconducting qubit arecapacitively coupled, thereby permitting a coupling to be performed onthe superconducting qubit and the superconducting bus; and a secondstate in which the superconducting bus and the superconducting qubit arecapacitively uncoupled.
 2. The quantum processing apparatus of claim 1wherein the superconducting qubit is a phase qubit, a charge qubit, aphase-charge qubit, or a quantronium qubit.
 3. The quantum processingapparatus of claim 1 wherein said quantum device is a CBJJ qubit, aphase-charge qubit, a quantronium qubit, or a charge qubit.
 4. Thequantum processing apparatus of claim 1, wherein said controllablecoupling mechanism comprises: a superconducting island; a Josephsonjunction including a first terminal and a second terminal wherein saidfirst terminal is coupled to the superconducting island; a gate voltagesource in electrical communication with said second terminal of saidJosephson junction and in electrical communication with ground; a firstcapacitor capacitively coupling the superconducting island to thesuperconducting qubit; and a second capacitor capacitively coupling thesuperconducting island to the superconducting bus.
 5. The quantumprocessing apparatus of claim 1 wherein said superconducting qubit is ina plurality of superconducting qubits and said controllable couplingmechanism is in a plurality of controllable coupling mechanisms, whereineach respective superconducting qubit in all or a portion of theplurality of superconducting qubits is controllably coupled to thesuperconducting bus by a respective corresponding controllable couplingmechanism in the plurality of controllable coupling mechanisms; and eachrespective controllable coupling mechanism in the plurality ofcontrollable coupling mechanisms is in any one of a plurality of statesat a given time, said plurality of states comprising: a first state inwhich the superconducting bus and the superconducting qubitcorresponding to the respective controllable coupling mechanism arecapacitively coupled, thereby permitting a quantum operation to beperformed on the superconducting qubit corresponding to the respectivecontrollable coupling mechanism and said quantum device; and a secondstate in which the superconducting bus and the superconducting qubitcorresponding to the respective controllable coupling mechanism arecapacitively uncoupled.
 6. The quantum processing apparatus of claim 5,wherein said portion comprises all the qubits in the plurality ofqubits.
 7. The quantum processing apparatus of claim 5, wherein eachrespective superconducting qubit in all or a portion of the plurality ofsuperconducting qubits is independently a phase qubit, a charge qubit, aphase-charge qubit, or a quantronium qubit.
 8. A bus architecture forquantum processing, comprising: a plurality of bus segments; a pluralityof qubit sets, each qubit set in the plurality of qubit sets comprisinga plurality of qubits; a plurality of pivot segments, each pivot segmentin the plurality of pivot segments controllably coupling a differentfirst bus segment and second bus segment in the plurality of bussegments to each other; and a plurality of controllable couplingmechanisms, each respective controllable coupling mechanism in theplurality of controllable coupling mechanisms controllably coupling acorresponding qubit in a qubit set in the plurality of qubit sets to abus segment in the plurality of bus segments such that each qubit ineach qubit set in said plurality of qubit sets is controllably coupledto at least one bus segment in said plurality of bus segments, whereineach respective controllable coupling mechanism in the plurality ofcontrollable coupling mechanisms comprises: a coupled state, wherein acontrollable coupling operation between a bus segment in said pluralityof bus segments and a qubit corresponding to the respective controllablecoupling mechanism is possible, and an uncoupled state, wherein thequbit does not capacitively affect the bus segment.
 9. The busarchitecture of claim 8, wherein a pivot segment in the plurality ofpivot segments is in electrical communication with a mechanism forcontrolling a characteristic of the pivot segment, and wherein the pivotsegment comprises: one or more controllable pivot segment couplingmechanisms, each pivot segment controllable coupling mechanism in theone or more pivot segment controllable coupling mechanisms couples thepivot segment to a corresponding bus segment in the plurality of bussegments and a pivot segment controllable coupling mechanism in the oneor more pivot segment controllable coupling mechanisms is characterizedby a first coupled state, wherein a controllable coupling operationbetween the bus segment corresponding to the pivot segment controllablecoupling mechanism and the pivot segment is possible, and an uncoupledstate, wherein the pivot segment does not capacitively affect the bussegment corresponding to the pivot segment controllable couplingmechanism.
 10. The bus architecture of claim 8, wherein a pivot segmentin the plurality of pivot segments is configured to pass quantuminformation between a first bus segment and a second bus segment in theplurality of bus segments.
 11. The bus architecture of claim 9, whereinthe mechanism for controlling said characteristic of the pivot segmentcomprises a quantum device.
 12. The bus architecture of claim 11,wherein the quantum device is a phase qubit, a charge qubit, aphase-charge qubit, or a quantronium qubit.
 13. The bus architecture ofclaim 9, wherein a pivot segment in the plurality of pivot segmentsfurther comprises: a plurality of subsegments, each subsegment in theplurality of subsegments controllably connected to another subsegment inthe plurality of subsegments by a controllable coupling mechanism andwherein two or more subsegments in the plurality of subsegments arecontrollably connected to different bus segments in the plurality of bussegments.
 14. The bus architecture of claim 13, wherein each respectivesubsegment in the plurality of subsegments is in electricalcommunication with a different mechanism for controlling acharacteristic of the respective subsegment.